given: 2 ≅ 5, ab ≅ de
prove: bc ≅ ec

Statements | reasons
1. 2 ≅ 5, AB ≅ DE 1. given
2. 3 ≅ 4 2. vertical angle thm.
3. △BAC ≅ △CDE 3. AAS
4. BC ≅ EC 4. CPCTC

thm. = theorem

CPCTC = Corresponding parts of congruent triangles are congruent

sorry if it looks a bit strange

 5 cm

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Explanation:

Recall that the range for cosine is from -1 to 1, including both endpoints. The smallest cosine value is what we're after, since we want the height to be as small as possible (to allow the blade be closest to the table).

Effectively, this means we replace the cos(x) with -1 so that it's as small as possible. Then we compute to get:

20*cos(x)+25

20*(-1) + 25

-20 + 25

5

The height of the fan tip is 5 cm when it is the closest to the table.

Side note: On the flip side, the furthest away the fan tip can get is 20*(1) + 25 = 45 cm. Therefore, the range of y values is